180-x=1/2x+9

Solution for 180-x=1/2x+9 equation:

180-x=1/2x+9

We move all terms to the left:

180-x-(1/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(1/2x+9)+180=0

We get rid of parentheses

-1x-1/2x-9+180=0

We multiply all the terms by the denominator


-1x*2x-9*2x+180*2x-1=0

Wy multiply elements

-2x^2-18x+360x-1=0

We add all the numbers together, and all the variables

-2x^2+342x-1=0

a = -2; b = 342; c = -1;
Δ = b2-4ac
Δ = 3422-4·(-2)·(-1)
Δ = 116956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116956}=\sqrt{4*29239}=\sqrt{4}*\sqrt{29239}=2\sqrt{29239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(342)-2\sqrt{29239}}{2*-2}=\frac{-342-2\sqrt{29239}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(342)+2\sqrt{29239}}{2*-2}=\frac{-342+2\sqrt{29239}}{-4}
$